> On 7 Feb., 08:53, Virgil <vir...@ligriv.com> wrote:> > In article> > <457d0429-33c1-46ad-9151-4f5d9dc96...@fv9g2000vbb.googlegroups.com>,> >> > WM <mueck...@rz.fh-augsburg.de> wrote:> > > On 7 Feb., 05:21, fom <fomJ...@nyms.net> wrote:> >> > > > Or as Virgil would write> >> > > in a very lucid moment:> >> > > > What Cantor proved was that no list of accessible real numbers> > > > (accessible because listable) can include all accessible numbers,> > > > because any such list itself proves the existence of numbers not listed.> >> > > That is, Cantor proved the countable set of accessible numbers being> > > uncoutable.> >> > That may well be WM's misunderstanding but it is not an understanding.> >> > A number being accessible does means that it can appear in some list,> > but does not at all mean that all accessible numbers can appear together> > in a single list.> > All elements of countable sets can be counted by definition, i.e.,> they can appear in a list.

But some subsets of a set may be countable even though the set itself is not. Certainly SOME sets of reals can be counted but not every set of reals can be counted.--